A particle moves on x-y plane according to the equations x = a cos (wt), y = b sin (wt).
1 - Show that its trajectory is an ellipse?
2 - Calculate the values of its velocity v(t) = |v(t)| and acceleration a(t) = |a(t)| ?
3 - What are the maximal and minimal values of v(t) and a(t) ?
I think for the first part the answer is as the following image. Please correct me if my answer is not right.
A particle moves on x-y plane according to the equations x = a cos (wt), y...
2. A particle moves in the x-y plane. Its coordinates are given as functions of time t(2 0) b x(t)-R(at-sina)t), )Sketch the trajectory of the particle. This is the trajectory of a point on the rim of a wheel y(t)-R(1-cosω t), where R and ω are constants. (a) (3 that is rolling at a constant speed on a horizontal surface. The curve traced out by such a point as it moves through space is called a cycloid. (b) (5 Find...
A particle moves in an elliptical orbit given by
?⃗=?cos???̂+?sin?? ?̂
where ? and ? are positive constants with ? < ?. Find the
speed and acceleration of the particle
as a function of time. At what time or times will the
acceleration be perpendicular to the velocity?
4. A particle moves in an elliptical orbit given by * = b cos wt î+ c sin wt where b and c are positive constants with c < b. Find the...
Consider a particle moving in the plane along the curve r(t) = (R cos(wt), R sin(wt)), where tER, for some constants Row >0. (i) (_marks:) Determine the distance the particle travels for t € [T, 47]. (ii) marks) Suppose the plane has a voltage given by V(x, y) = xy +3. Determine the rate of change in voltage the particle experiences at time t.
According to the given equations of motion of the particle M determine the type of trajectory and for a moment of time t=t_1, find its position on the trajectory, its velocity , total tangential and normal acceleration , and a radius of the trajectory curvature. a) X=-2t^2+3,(cm), Y=-5t(cm) , t_1=0.5(s) b) X=-3/(t+2), Y=3t+6, t_1=2
A particle moves in the x-y plane such that its position is defined by r (2t i+ 4tj) ft, where t is in seconds. Determine the radial and transverse components of the particle's velocity and acceleration whent-2 s.
3) A particle moves in the xy-plane with velocity v (m/s) for time t (s) according to u = (6t-4t2)1+ 9). a. Determine the direction of the particle at t 1.5 s in terms of an b. Determine the time or times (for t>0s) when the velocity is zero. If it c. Determine the x-component and y-component of acceleration at d. Determine the time or times (for t>0s) when the acceleration is zero. angle with respect to the x-axis. is...
2) A particle moves in the x-y plane. Known information about the particle’s motion is given below: ???? = 150?? ft/sec. and at time t = 0, x = 6 ft ?? =5??3+50?? ft a) Derive, as functions of time, the position (x), acceleration (ax), velocity (vy), and acceleration (ay). b) Using your functions, calculate, at time t = 0.25 seconds, the total magnitude of velocity ?? of the particle and the angle ????the velocity vector makes with the x-axis....
A particle moves along the x axis according to the equation x = 2.06 + 2.95t - 1.0062, where x is in meters and t is in seconds. (a) Find the position of the particle at t = 2.80 s. m (b) Find its velocity at t = 2.80 s. m/s (c) Find its acceleration at t = 2.80 s. m/s2 Submit Answer
Le Problem 3.3 The motion of a particle is defined by the equations x=(4cos -2) (2 - cos act) and y =(3 sin TI)/(2 - cos al), where x and y are expressed in feet and / is expressed in seconds. Show that the path of the particle is part of the ellipse shown, and determine the velocity when (a) / -0. (b)/ 1/3 s, (c) 1 = 1 s.
A particle moves along the x-axis so that its velocity at any time t/geq0 is given by v(t) = 1 - sin(2t). (a) Determine the expression for acceleration at any time t. (b) Find all values t, 0 <t<2, for which the particle is at rest. (c) Determine the expression for the position Jf the particle at any timet if x(0) = 0.